Speaker: Mr Patrick Laub, UQ

Modern financers and insurers need to understand the risk they own in their portfolios, and to estimate the chance of a catastrophic loss or bankruptcy. Even with the most basic models (such as those of Black & Scholes or of Cramér & Lundberg) simple quantities such as quantiles are impossible to calculate directly. In my PhD, I have worked on density and Laplace transform approximation for the distribution of the sum of lognormals. Recently, with Pierre-Olivier Goffard, we have generalised the density approximation method (which relies on an orthogonal polynomial expansion) to general random sums. I'll outline the numerical aspects of the work, which includes quasi-Monte Carlo integration with importance sampling, and symbolic differentiation within Mathematica’s infinite precision algebra. The papers covered are available on Patrick's website.

About Statistics, modelling and operations research seminars

Students, staff and visitors to UQ are welcome to attend our regular seminars.

The events are jointly run by our Operations research and Statistics and probability research groups.

The Statistics, modelling and operations research (SMOR) Seminar series seeks to celebrate and disseminate research and developments across the broad spectrum of quantitative sciences. The SMOR series provides a platform for communication of both theoretical and practical developments, as well as interdisciplinary topics relating to applied mathematics and statistics.